Dynamic proportional edit connected to an object?
Two possibilities (at least) : hook modifier and vertex weight proximity + shrinkwrap.
And an edit using dynamic paint (following the comments).


Hook modifier :




The setting is the following :

The hook modifier is defined for the plane, and an empty is use as a hook. You can tune the falloff and the proximity. You must define a vertex group (assign the wanted vertices to it).




Vertex weight proximity and shrink wrap :


This can be a more dynamic solution.

First add a vertex weight proximity modifier. That will assign to the vertex group a value depending on the distance to the empty.
Then add a skrinkwrap (targeting to another plane) and using this vertex group.

You need to define another plane to skrinkwrap to (this plane is placed near to the surface... not visible here as it is in wire display mode).








A third solution using dynamic paint :


The object is in wireframe here to allow to see the moving object (here spheres replace that was empties previously).



The principle is the same, as before but the weights of the vertex group are given using dynamic paint.

Configuration for the spheres used as brushes : here 'proximity' is used (other options available) and you have also some option for the falloff.



Configuration for the grid : we are painting on 'weights' on the vertex group.



And as before the grid has a shrinkwrap using the same vertex group :



Updated blend file :